Method of and means for increasing the useful low flow capacity of a hydroelectric plant



July 7. 1931.

F. A. ALLNER LOW FLOW CAPACITY OF .A HYDROELECTRIC PLANT Filed Nov. 30, 1929 14 Sheets-Sheet l c I C & f

mm I m A S g i V v 1 I 1L- 1 Low can? THERMAL 40v- ?ENERGY 7 v: L. 87% C 3\/// D A X W B '"--E, l-

i .3 5 HOURS AM. PM. o MNT. 6 M 6 MIT.

FIGJ FIGJG a 3. B a D.

d h. 3 min 3 DAYS ORPEHCENT orrmcorvm A DAYS URPERCENT OF TIME OFYEAR J FIG. 3

INVENTOR ATTORNEY F. A. ALLNER 1,813,107 IBTHOD 0! AND IBANS FOR INCREASING TBS USEFUL 14 Shuts-Sheet 2 July 7. 1931.

my now cumcn! or A lumwanncram rum FilQd Nov. 30. 1929 July 7. 1931. F. A. ALLNER 1,813,107

-- IETBOD 01mm IEANS' FOR 'mcmusmo ranusnm v now my CAPACITY or A- nnnosnscrnrc run! 14 Shoots-Sheet 3 Filed Nov. so. 1929 QQE B July 7. 1931. F. A.-ALLNER IETHOD OF AND IIEANS FOR INCREASING THE USEFUL LOW FLOW CAPACITY OF A HYDROELECTRIC PLANT,

Fil'ed Nov. 30. 1929 14 Sheets-Sheet 4 1' Y 'so I P I: I I F I I l V I,

KILOWAT T8 K ILOWATT HOURS PER YEAR 30 no I l0 0 w 0 I 0 %5DEED 0F EgJAL EFFICIEKIY 5 SEED (F EQLLEF'E .INVENTOR I FIG. m 9

' A. mman 1,813,107 BT50!) AND IEAIIS 1'01! INCREASING I!!! USEFUL L0! 1')! CAPACITY 0!" A HYDROBLBCTRIC PLANT Filed Nov. 30. 1329 14 Sheets-Sheet 5 July 7. 1931.

. 60 '10 80 90 I00 I I loSPEED OF EQUAL EFFICIENCY FIG. IO

DISCHARGE a0 83 I00 [IO 1 I20 9'6 SPEED OF EQUAL EFFICIENCY I00 56m: OPENING I N VEN TOR FIG |o-b BY F. A. ALLNER July 7, 1931. u I 7 1,813,107

muon or m Isms ron mcnnsmu ran ussmn 1.01pm! canon! "or A mnRoaLn-c'mm rum-r 14 Sheets-Shoat 6 Filed NOV. 30, 1929 INVENTOR.

omvzy July 7., 1931. L E 1,813,107

IETHOD OF AND IEANS FOR INCREASING THE USEFUL LOI FLOW CAPACITY OF A HYDROBLBCTRIC PLANT Filed Nov. 30. 1929 14 Sheet-meet 7 Q E w H I N VEN TOR July 7. 1931. 1 v|'-', ALLNER 1,813,107

much or mm Imus FOR INCREASING was USEFUL now no! CAPACITY or A mnnonmc'mxc rum Filed Nov. 30. 1929 14 Sheets-Sheet 8 F. A. ALLN ER July 7. 1931.

IETHOD 0! AND IEANS FOR INCREASING THE USEFUL LOW FLOW CAPACITY-OF A HYDROBLBCTRIC PLAN! 14 Sheets-Sheet 9 F1106 Nov 30. 1929 IN VEN TOR.

. @Z RNEY.

July 7. 1931. F. ALALLNER 1,813,107

- IETHOUOF AND HANS FOR INCREASING Ta! USEFUL Lb" FLOW CAPACITYOF A HYDROELECTRIC PLANT" l4 Sheets-Sheet 11' Filed Nov. 30. 1929 -IN T0R1 7 fiomvsv July 7. 1931. F. A. ALLNER 1,313,107

IETHOD 0! AND MEANS FOR INCREASING THE USEFUL LOW FLOW CAPACITY. OF A HYDROELECTRIC PLANT Filed Nov. 30. 1929 '14 Sheetd-Sheet 12 1N VEN TOR y 1931- w F. A. ALLNER 1,813,107

. IETBOD 01' AND BANS FOR INCRBASIIG Q USEFUL LOW FLOW CAPACITY OF A HYDHOELECTRIC PLANT Filed Nov. 30. I929 14 Shoots-Sheet l3 INVENTOR.

A TTORNE Y.

F. A. ALLNER July 7, 1931.

,4 1,8135107 xnrnon or 1mm nuns FOR mcnmsme was USEFUL LOW FLOW CAPACITY OF A HYDROELECTRIC PLANT Filed .Nov. 30. 1929 14 Sheets-Sheet l4 INVENTOR. W

ATTORNEY.

Patented July 7, 1931 UNITED STATES PATENT- OFFICE FREDERICK A. ALLNEB, OF BALTIMORE, MARYLAND METHOD OF AND MEANS FOR INCREASING THE USEFUL LOW FLOW CAPACITY OF A HYDROELECTRIC PLANT Application filed November 30, 1929. Serial No. 410,818.

This invention refers to a new and improved method of and apparatus for increasing the efi'ective capacity of a hydro-electric generating station in an interconnected steam and hydro-electric system during periods of low flow by converting low-cost oil-peak electric energy, either steam or hydro, into hydro power capacity of high value, without the use of a storage reservoir at a is level higher than that of the headwater pond of the hydro plant and without the use of pumps other than the hydraulic turbines.

This is accomplished by operating a portion or all of the turbine generator sets at the .1 hydro plant as motor driven pumping sets for pumping water from the tailwater pool into the headwater pond during the hours when this hydro plant is not generating, and subsequently discharging this water through 29 the turbines during hours of generation, thus iricrcasing the peak generation at the hydro i) ant.

A major object of the invention is to make economically feasible the development of water power on rivers with fluctuating stream flow and pronounced low flow stages by increasing the low flow capacity value with a minimum of additional investment and a relatively small amount of energy losses, incident to conversion of low cost off-peak energy into high value peak energy.

Another object of the invention is to increase the effective capacity availableunder minimum flow conditions at existing hydroelectric plants that now have machinery installed with capacity in excess'of the present effective capacity usable under minimum flow conditions, and thereby increase the economic value of such plants.

Another object of the invention is to make profitable additions to the existing genera-ting capacity at plants where all of the installed generating units are now usable as effective capacity under minimum flow conditions, this invention making possible an increase in effective capacity at low increment investment cost per unit of capacity and at small operating expense, and

yielding at the same time additional energy output from the additional water-wheel capacity during high flow periods.

A still broader object of the invention is to accomplish a more perfect coordination of of an interconnected system the most economical method of operating the hydro and steam plants for maximum capacity value, and a more comprehensive scheme of developing the remaining Water power sites of this country, some of which it W ould not be cconomically feasible to develop at all without this invention.

Another object of this invention is to pro vide simple and efficient means for applying this method, either in existing plants at a small amount of investment or in additions to existing plants, or in a more economical design of undeveloped water power sites.

Other ob'ects and advantages will become apparent rom the specification, taken in connection with the accompanying drawings,

wherein the invention is embo form.

Fig. 1 is a typical load dia of heavy load on an electric died inconcrete gram for a day power system,

supplied with steam and water power, showing also the distribution of load between the two sources of power at times of minimum natural river flow at the water power plant.

Fig. 1a is a loaddiagram for the same day as Fig. 1, drawn as summation curve and having auxiliary curves drawn in which indicate the ain in useful capacity that is obtainable y this invention at mum'river fiow.

times of mini- Fig. 2 is a typical hydrograph in the shape of a summation curve, showing the run-off in cubic feet per second per square mile of drainage area in relation to the number of days in the average year that such run-off is available.

Fig. 3 is a diagram showing the average amount of hydro-electric energy that is available from a hydro plant located on a river with run-oil conditions, as per Fig. 2, and also that portion of the energy that is usable on a load system corresponding to Fig. 1.

Fig. 4 is a plan view of three water power plants located serially on the same river, the headwater level of one plant forming the tailwater of the next higher plant, the intermediate plant having no pondage, the upper and lower plants equipped with pondage.

Fig. 4a is a longitudinal section and elevation of the three water power plants shown in Fig. 4, on line 4a4a of Fig. 4.

Fig. 5 is a, plan view of two pondage equipped water power plants, located on the same river, the headwater level of the lower plant forming the tailwater of the upper plant.

Fig. 5a is a longitudinal section and elevation of the two water power plants shown in Fig. 5, on line 5a-5a of Fig. 5.

Fig. 6 is a larger scale reproduction of the low flow section of energy diagram of Fig. 3, showing also relationship between 24 hour capacity and equivalent days of energy deficiency at that capacity.

Fig. 7 is a group of curves showing a method of determining the economic relation between increased capacity value of va plant, cnerg .gain in high flow and pumping energy loss in low flow.

Fig. 8 shows in curve form efficiency and capacity of a six stage high head pump of low efiiciency, functioning either as turbine or as pump over a wide range of speed, operating under a. constant head.

Fig. 9 shows in curve form efficiency and capacity of a single stage Francis type low head pump, of medium efiiciency, functioning either as turbine or as pump over a wide range of speed, operating under a constant head.

Fig. 9a is a group of velocity diagrams" at entrance when the centrifugal pump of the characteristics shown in Fig. 9 is opprated as turbine with and without mova vanes.

Fig. 9b is a group of velocity diagrams at exit when the centrifugal pump of the characteristics shown in Fig. 9 is operated as turbine wit-h and without movable guide vanes.

Fig. 10 shows in curve form efliciency and le guide capacity of a medium head Francis type tur-' bine, functioning either as a turbine or as pump over a wide range of speed, operating under a constant head.

Fig. 10a shows in curve form relation of speed and discharge for a turbine of the characteristics shown in Fig. 10, when operatedas pump at, 10%, 30% and gate opening.

Fig. 10?) shows relation between gate opening and speed of impending delivery for a turbine of the characteristics shown in Fig. 10, when operated as pump either with a short elbow intake or with a spiral or with a long conical intake. Fig. 11 shows velocity diagrams at entrance andexit for a turbine with movable guide vanes, when operated as pump near speed of impending delivery.

Fig. 11a shows velocity diagrams at entrance and exit for a turbine with adjustable rotor blades, when operated as pump near speed of impending delivery.

Fig. 12 shows the wiring diagram of an electrical machine, suitable for operation at two frequencies, with reversing switches of field and armature windings in position for operation at the higher frequency.

Fig. 12a shows the wiring diagram of the same electrical machine as in Fig. 12, with reversing switches of field and armature windings in position for operation at the lower frequency.

Fig. 13 shows the wiring diagram of an electrical machine suitable for operation at two speeds, with reversing switches of field and armature windings in position for operation at the lower speed.

Fig. 13a shows the wiring diagram of the same electrical machine as in Fig. 13, with reversing switches of field and armature windings in position for operation at the higher speed.

Fig. 14 is a cross-sectional elevation of a radial flow turbine with adjustable blades, suitable for operation as turbine or as pump.

Fig. 14a is a plan view of the rotor of a radial flow turbine, with the coverplate of the hollow hub removed.

Fig. 146 is a cross-sectional elevation of a radial flow turbine with adjustable blades showing link connection blade arm and adjusting spider.

Fig. 140 is a plan view of a radial flow trubine with adjustable blades showing link connection between blade arm andadjusting spider.

Fig. 15 is a partial cross-sectional elevation of the upper portion of. the main turbine shaft with control motor and blade position indicator.

Fig. 15a is an enlarged sectional plan view on line 15a15a of Fig. 15.

Fig. 16 is a cross-sectional elevation of a diagonal flow turbine with adjustable blades suitable for operation as turbine or as pump.

Fig. 16a is a plan view of the rotor of a diagonal flow turbine, with the cover plate of the hollow hub removed.

In order to better illustrate the scope of this invention and means by which same is accomplished, a brief review of recent trends in power development and of the chief economic considerations underlying the most effective use of difi'erent sources of power will be necessary.

The high investment cost of modern steam plants and the demand of industries to secure the lowest possible rates, are gradually replacing the formerly isolated local power systems by large interconnected networks comprising a number of thermal plants,

water power plants and long distance trans mission systems. The load demand on such a system varies a great deal during the different hours of the day and during the days of the week and different seasons of the year but, on the whole, these variations can be fairly well anticipated and are more or less regular. Forexample, during the hours between 11:30 p. m. to 6:30 a. m., the load demand is only a small fraction of the load requirements during the day hours on weekdays when th'e factories are running and when railways move traffic. A typical daily load curve is shown in Fig. 1, referring to the period of the year when the day peaks are nea'rlythe highest of the season and when in theyears of low rainfall the river flow.

maybe near to the minimum that ever-occurred in prevlous low flow periods. The

" lowest load of the day occurs early in the morning, around 3:00 a. m., as indicated by point B in Fig. 1; thehighest load or peak.

otthe day occurs between 5 :00 and 6 :00 p. m.,

as indicated by point C in Fig. 1.

Veryfew such load systems obtain their entire requirements from water power alone,

and the great majority supply their load .re-

quirements with power generated partly by Water, partly by steam and internal combustion engines. The most effective way of utilizing water power developments, subject to wide variations in available water supply, in the interconnected load system is to .let the hydro source of supplyfurnish-the base portion of the load during the wet seasons when there is ample flow and the output of the plant is. limited not. by flow but by installed generating capacity, and let. the ther- 'mal plants carry the peak portion of the load- During the low flow season this dis-.

tribution is reversed, i. e., the output of the water power plant, which is greatly reduced below that available during the wet season,

is carefully distributed into the peak portion of the load curve so as to furnish the greatest capacity service with the limited amount of energy, whereas the thermal plants operate on the base portion of the load.

' Fig. 2-is a typical yearlyhydrograph representing average run-oti in cubic feet per second per square mile of drainage area. Fig. 3 is the same typical hydrograph shown in Fig. 2, redrawn to a kilowatt scale for a given head and plant efficiency. The line ABD in Fig. 3 gives the 24 hour power available from natural inflow. Using the typical daily load curve of Fig. 1, the line ABX of Fig. 3 can be drawn representing the usable energy. Available and usable power are the same up to point B ofFig. 3, corresponding to point B, the lowest load of the day in Fig.

1. The horizontal distance between the lines BD and BK is potential energy wasted during the hours of low energy requirements.

For any given water power site the maxiage river year will be approximately proportional to the head, drainage area and run-off per square mile, independent of the amount of generating capacity installed, as long as there is not suflicient flow to operate the entire installed machinery at full capacity.

. i 90 mum energy that may be obtained in an aver- This isithe low flow period indicated on the left portion of Figs. 2 and 3. \Vhen there is more water in the river than can be converted toelectrio power by the installed generatorcapacity and utilized in the load systems, i. e., during the high flow period, the maximum available output of theplant will remain practically constant, as indicated by the horizontal dotted line M(M) in Fig. 3, except that at times of very high flood stages a reduction of head will usually be experienced, which has a tendency to reduce-the available output during a few days of the year, represented by the extreme right portion of Figs. 2 and 3.

On pondage equipped hydro plants the power will be drawn at a steady rate during the 24 hours, as far as it'can be used by the load, only during the high flow period. During the low stages of the river and especially at times of minimum flow, the water will be discharged through the power house during l the hours of heavy load demand only, so as to render the greatest capacity service to the system within the limits of the available hydro energy as indicaed in the cross-hatched areas at the top of Fig. 1 above the horizontalline Ab.

For a given amount of minimum flow hydro energy this capacity service will bethe it will be possible in many cases to secure a larger amount of low cost thermal energy dunng the ofl-pe'ak-hours than indicated by the cross-hatched area of Fig. 1, and use such energy for pumping purposes at the hydro plant. The total amount of such pumped energy will then be limited by the capacity of transmission lines and transformers connected to the hydro plant, or by the motor input of the pumping sets, whichever is lower.

' however, discharging only the natural in- Figs. 4 and 4a are an example-of three plants in series on the same river, the tailrace of each upper plant forming the headrace of the next lower plant. The uppermost and lowest plants are assumed to have considerable pondange, whereas the pool formed by the dam of the intermediate plant is assumed to be small, being not more than thesurface of the headrace canal. Modern dam structures, equipped with regulating gates for the discharge of flood waters, often have a few feet of free-board for the purpose of avoiding spilling of water due to wi d at normal operating level. The dams whic 1 are not designed with such flood gates can be easily equipped with fiashboards or other temporary crests at very small cost. These temporary crests need be maintained only at times of very low river flow and can be readily removed during higher stages of the river. 'Figs. 5 and 5a are an example of two plants in series on the same river. I I

The plan of operation contemplated under this invention will be to discharge, at times of very low river flow, a greater amount of water from the two upper plants than the natural inflow; to accumulate this excess discharge in the pond of the lowest plant, the latter,

flow. During the off-peak hours when none of the hydro plants is generating, I propose to use the otherwise idle generating machincry of the two upper plants as pumping machinery to lift the water, discharged in excess of natural inflow during the generating period, from the lower ponds back'to the pond of the uppermost plant. The power necessary for this pumping operation is secured from the otherwise unused but available capacity of the thermal plants or of water power plants, having excess flow, forming part of the interconnected power system.

Under average conditions power will be available forpumping during six to eight hours on week days and approximately during the whole twenty-four hours on Sundays.

Ifthe ponds are sufficiently large, it will be. a lowering of the water level in the upper .180

possible therefore, to operate instead of on a daily cycle of generation on a weekly cycle,

thus increasing in effect the daily excess discharge by an amount equal to approximately one-sixth of the water that can be pumped back during the twenty-four hours of Sunday operation. I

A large part of the investment in water power plants consists of the costs of dam, property, relocation of railroads, bridges, highways, etc., i. e., a fixed amount, independent of the number of generating units. The increment cost per kw. of installed capacity, including the pro-rated cost per kw. of transmission lines and tie-in'equlpment, but exclusive of the fixed cost for propert dam and other hydraulic structure, is usual (1? lower than the increment cost per kw. of a ditional steam capacity.

Heretofore,it has been the practice to install hydro-electric capacity for a relatively small run-off per square mile, the upper limit of capacity being a proximately determined by the economic balance between annual charges on the hydro investment and the useful hydrocapacity under minimum flow con ditions, at the equivalent cost per kw. of steam investment, plus the ener 'y value on the basis of steam cost-s of that mount of hydrooutput which is obtainable by the total installed capacity.

The purpose of this invention is to greatly increase on pondage equipped hydroplants, located serially on the same river, the useful capacity obtainable from such hydro plants at times of minimum =flow. In order to obinvention in the case of undeveloped water power sites, it will, therefore, be necessary to determine in advance the limiting conditions that are imposed by certain natural characteristics of a given development.

These limitations are'infl uenced largely by a number of factors, any one of which may control the upper limit at which regeneration ceases to be rofitable; the factors are:

(1) Capacity of pondage, available for regenerative operation. g

(2) Amount of pumping power and number of pumping hours during each cycle.

(3) Relation of power input when pumping to power. output when generating, i. e., efficiency of regenerative conversion.

(4) Relation of increment cost of additional hydro capacity, including transmission investment, to increment cost of steam capacit (5) Relation 'of the duration of deficiencies in flow to the duration of high flow stages usable by the additional capacity installed, i. e., the relation between energy consumed in high fiow.

pond in excess of the natural inflow will cause pond and a raising in the lower pond. The decrease in the upper plus the increase in the lower pond represents the reduction in head, under which the upper plant will operate at the end of the drawdown period. The lower plant will operate during the whole drawdown period at a gradually increasing head, the maximum at the end of the drawdown period being equal to normal operating head plus the maximum rise in the lower pond. Thus, there will be on the average a lowering in the combined effective operating head of the two plants, i. e., a reduction in output from natural inflow alone, below that obtainable from the same water under normal head conditions.

Assuming that there will be no physical limitations, other than those controlled by practical operating conditions, along the shores of the lower pool (railroads, highways, buildings, etc.), or at the power house structure itself, we may expect that the excess drawdown may be carried to a point, where either an excessive lowering of head renders turbine operation at the upper plant too inefficient or impractical or where the increased capacity at the lower plant would overload the generators. The limit will probably be first reached at the upper plant and approximately at that head which is the capacity controlling one at times of very high flood stages. Under average conditions this maximum practical reduction of head will be of the order of approximately 40%. Instead of expressing this useful pondage in absolute terms of million cubic feet or in cubic feet per second average flow during 24 hours, I will refer to it henceforth in relation to minimum natural inflow, calling the ration between the two (X), which will have a bearing on the net gain of energy that can be secured over a wide range of pond ratios, i. e., relation of upper pond area to lower pond area.

This net gain N in kwh. is independent of the head at the lower plant. I express same in the following general equation:

in which both ponds of same characteristics, ower pacity.

Per ce'nt Per cent Per cent 80 80 80 Unlimited upper pond Upper and lower pond identical. Unlimited lower pond (2) It is evident that regardless of the amount of regenerative pondage that may be available at a water power site, at practically no increase in investment costs, only such portion of it can be employed for purposes of additional hydro generation during peak hours as can be refilled by pumping during the 0dpeak hours. Where the usable pondage is relatively small, perhaps equal to or smaller than the natural inflow, it will usually be possible in the cases that I have investigated, to employ the entire pondage for regenerative purposes even at comparatively low conversion efficiencies.

In the great majority of other cases, however, a preliminary investigation will be necessary to determine the approximate amount of available regenerative pondage that can be made use of by reason of limitations in pumping capacity and available pumping energy. Ihe maximum amount of water that can be lifted back by pumping in the case of a power system that has no interconnection with neighboring systems, will be limited by the following conditions 7 Capacity of generators when operating as motors;

Amount of off-peak thermal energy;

, Average efliciency of conversion.

I worked out a simple graphic method in Fig. 1a on the example of load curve of Fig. 1 for three assumed values of conversion efliciencies, 40%, 50% and 60%. In Fig 1a the cross-hatched upper portion of the load curve (developed as a summation curve from Fig. 1) represents the amount of peak load supplied by the two hydro plants at times. of minlmum natural inflow. --The upper lant contributes the amount of 0min as use 111 capacity. We may also assume that a certain amount of additional capacity Cl will be provided, justified by its'energ yield during high flow and by certain considerations of reserve capacit during highest flood stages,

etc. The tas is to determine the amountof further capacity C justified by regenerative pondage.

At point A on the left side of Fig. lo I plotted a curve which, in horizontal distance from the line 0A to the right, equals the load area for any point below ab. Thus, for point I, lying a certain amount of kw. below A, the

plotted from point B, which represents the minimum load at any time of the day, a similar curve drawn to the same scale as the curve plotted through A as a starting point, the horizontal distance of which, at a given vertical distance above B,'is equal to the assumed conversion efficiency times the area at the left of the load line. Thus, for an arbitrary point J the horizontal distance J (J) equals the area. J 'B times the conversion efliciency. Three values of conversion efiiciency have been assumed, 40%, 50% and 60%. I thus obtain three curves, starting at B and extending in an upward right direction and intersecting with the curve that started at point A in a downward direction to the right. The vertical distance from these points of intersection to the horizontal line going through A, is a measure of the additional capacity that can be made use of during minimum flow for the three different conversion efliciencies assumed. The vertical distance from these same points of intersection down to a horizontal line drawn through point B is a measure of the motor input necessary for pump ing. The horizontal distance from these points of intersection, X X and X to the vertical line A0 is ameasure of the additional peak generation that can be supplied to the system at the conversion efliciency of 40, 50 and 60%, respectively By recalcula-ting this electrical energy in terms of cubic feet, under proper assumptions of efficiency of generation, average head, etc., I can determine with a fair degree of accuracy the amount of pondage necessary for this. additional discharge of water for the different conversion efiiciencies assumed.

A further check may be made as to the adequacy of motor capaclt available for pumping. As the curves s ow clearly that the lower the efficiency of conversion the greater the motor input, and the lower the additional ,useful peak service, I need investigate only conditions of greatest pump motor capacity, i. e., lowest eiiiciency, and make sure that even for that condition the generator capacity 0min plus C plus the regenerative capacity or gain due to pumping (i will furnish sufficient motor capacity. As generating e uipment is designed for power factors of mm to 90%, on the average approximately 85%, whereas motors can be operated at unity power factor we would expect to find in most cases sufiicientfmotor capacity available. If, however, the load curve at point B should be relatively low, whereas point A lies rather high, it may be possible that for some of the lower efiiciency curves a correction must be made, starting from B, to take into consideration the limited pumping capacity.

In the case of a power system that has large capacity interconnections with neighboring systems, the amount of low cost off-peak thermal energy available for pumping need not be limited to that originating on the power system for which the loadcurve of Fig. 1a is drawn. It will be possible then to disregard the area above the load curve, starting at point B as a limiting factor of available pumping energy and instead merely check up at what distance!) below horizontal line Ab, a point can be located on load integration curve A(A), where the product of the hours of pumping times times conversion efliciency will approximately equal the horizontal distance of that point from the vertical line 0A. These new points of intersection with curve A(A) are Y405 Y and Y in Fig. 1a, the vertical distance upward to horizontal line Aa representing the gain in useful capacity C,,, made available by regenerative pumping on a power system having large capacity interconnections with neighboring systems.

(3) The third factor next in impbrtance, having a bearing on the extent to which it is practically possible and economical to apply my invention and install additional generating capacity of the dual service type for exploitation of pondage, is the efliciency of conversion. This will be the product of several individual efiiciencies, viz :1

High Low (a) Transmission from thermal plants to low ten- Per cent Per cent sion bus of hydro plant 95 85 (b) Generator, operating as driving motor at unity power factor 97 95 (0) Turbine, operating as pump 85 60 (:1) Starting and stopping 97 90 (e) Slope of pond, head loss through racks, etc.,

when pumping 99 97 (I) Slope of pond, head loss through racks, etc.,

when generating 99 97 (q) Turbine 90 80 (h) Generator 96 94 (i) Transmission from hydro plant to low tension bus of thermal plants 95 85 Product of all efliciencles (a) to (1') incl... 61. 1 26. 2 Product of efliclenc'ies (b) to (h) incl 67. 7 36 3 As the load curve in Figs. 1 and 1 has been stepped up by the transmission losses, the

combinedefliciencies of.67 .7 to 36.3 represent the probable range of overall efficiencies to be considered. For the otherinvestigations of limitations (4) and (5), however, the transmission losses ((1) and (6) must be taken into account.

(4) The increment cost per kw. of hydro capacity including transmission and tie-in investment and adjustment for loss in transmission, may vary over a much wider range than the cost per kw. of steam capacity. This is due to the great variations possible in the distance of transmission, diflerencesin head, etc. However, evenfor low head plants of approximately 50 ft. fall, and for distances 

